Can a U.S. Resident go to college in anouther country? If so, how?

The first test of if you are qualified to attend a school is if you can figure out how to apply. Having your mommy help you is an automatic fail.

The education won't be as good, she would have to learn another language and customs, not to mention the travel costs. Better she stays in USA.

Ummm no, because 1) she'll probably need a visa

2) When you are granted Permanent residency you intend to live, work, or maybe even go to school in the US. Sure, you can travel abroad and freely return but if you stay outside the US for longer than 6 months you're going to have to see an immigration judge to prove you didn't abandoned your residency.

Sure, but she will get spit in her face because no one likes you dumb Americans.

Yes. Talk to the school and the country's immigration. She'll need a student VISA.